Approximation algorithms for the geometric covering salesman problem
Discrete Applied Mathematics
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
A fast approximation algorithm for TSP with neighborhoods
Nordic Journal of Computing
Beyond Steiner's Problem: A VLSI Oriented Generalization
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
TSP with neighborhoods of varying size
Journal of Algorithms
Approximation algorithms for euclidean group TSP
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-sixth annual symposium on Computational geometry
Efficient data collection from wireless nodes under the two-ring communication model
International Journal of Robotics Research
An evolutionary approach for the dubins' traveling salesman problem with neighborhoods
Proceedings of the 14th annual conference on Genetic and evolutionary computation
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In the TSP with neighborhoods problem we are given a set of n regions (neighborhoods) in the plane, and seek to find a minimum length TSP tour that goes through all the regions. We give two approximation algorithms for the case when the regions are allowed to intersect: We give the first O(1)-factor approximation algorithm for intersecting convex fat objects of comparable diameters where we are allowed to hit each object only at a finite set of specified points. The proof follows from two packing lemmas that are of independent interest. For the problem in its most general form (but without the specified points restriction) we give a simple O(logn)-approximation algorithm.